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<article class="li"><h3 class="heading">
<span class="type">Item</span><span class="period">.</span>
</h3>
<p>If <span class="process-math">\(f(x)\)</span> is an odd, periodic function with <span class="process-math">\(2L\text{,}\)</span> it has a <dfn class="terminology">Fourier sine series</dfn></p>
<div class="displaymath process-math" data-contains-math-knowls="">
\begin{equation*}
\hat{f}(x)=\sum_{n=1}^{\infty}b_n\sin\frac{n\pi x}{L},
\end{equation*}
</div>
<p class="continuation">where</p>
<div class="displaymath process-math" data-contains-math-knowls="">
\begin{equation*}
b_n=\frac{2}{L}\int_{0}^{L} f(x)\sin \frac{n\pi x}{L}~\textrm{d}x,\qquad n=1,2,3,\cdots
\end{equation*}
</div></article><span class="incontext"><a href="sec7_5.html#li-48" class="internal">in-context</a></span>
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